In the expression |a:sxy,b:SXY|, "a" and "b" are numbers for fundamental matrices which are listed in the following part. The numbers (x,y) and (X,Y) mean the displacements of the elements. Therefore, the matrix element for a:xy is given by such that is one of fundamental matrix. s and S mean symmetrical transformations summarized in the following table.
For example, the matrix element for a:3xy is an element of a fundamental matrix. The above symmetrical transformations cover of symmetries. These results are calculated by the awk script. Prof. Suzuki's "ultra-super" magic squares are also decomposed, which leads to only two fundamental digit-matrices (here).